A systematic density functional study of the adsorption and dissociation Of O-2 on the (001) surface of several transition metal carbides (TCMs; TM = Ti, Zr, Hf, V, Nb, Ta, Mo) is presented. It is found that O-2 may adsorb molecularly on two different sites with similar adsorption energy. At these sites, either O-2 bridges two surface metal (M) atoms or it is placed directly on top of a M surface atom. A case apart is delta-MoC, where O-2 adsorption on top of surface Mo atoms is far up in energy with respect to bridging two surface Mo atoms. The relative stability of O-2 on these TMCs is dominated by the electron back-donation between the surface and O-2 and the stabilization of the resulting partially charged molecule by the surface metal sites. Three reaction paths leading to O-2 dissociation have been considered. The first reaction pathway starts from M-M bridge molecular adsorption and lead to O atoms on top of surface M atoms (TSM) and the second one (TSC) starts from on top molecular adsorption and lead to final states where O atoms are adsorbed on 3-fold hollow sites neighboring two M and one C surface atoms, while the third pathway (TSBC) starts from O on the M-M bridge and leads to TSC products. For each reaction path, transition state structures have been located and the corresponding energy barriers obtained. At low temperatures, O-2 dissociation on group IV TMCs can only occur via the TSBC pathway whereas at high temperatures it may also take place starting through TSc. For the rest of the carbides, only TSC and TSM paths are possible. The calculated transition state theory rate constants reveal that TMCs of groups IV and V are easy to oxidize whereas this is especially difficult for delta-MoC. The rate constant trends follow the calculated energy barriers and explain the oxygen preference for carbon on group TV TMCs and delta-MoC, as well as the preference for metal atoms on group V TMCs.